Thermal capillary waves relaxing on atomically thin liquid films

Atomistic simulations are used to investigate the relaxation dynamics of thermal capillary waves on thin flat liquid films. Short Lennard-Jones polymers (n=2, 4, and 8) model the liquid in films of thickness 6 sigma to 96 sigma, where sigma is the Lennard-Jones atomic length-scale parameter. Assuming no-slip boundary conditions on the solid wall and constant surface tension and viscosity, the standard continuum model predicts that capillary waves decay with rates omega that scale with wavenumber q as omega similar to q(4) for long wavelengths and omega similar to q for short wavelengths. The atomistic simulations do indeed show these scalings for ranges of q, and, of course, this model must fail for large q as wavelengths approach atomic scales. However, before a complete breakdown of the continuum description, an unexpected intermediate regime is found. Here the decay rates follow an apparent omega similar to q(2) power law. The behavior in this range collapses for all the cases simulated when q is scaled with the radius of gyration of the polymers, indicating that a molecular-scale effect underlies the relaxation mechanics of these short waves. (C) 2010 American Institute of Physics. [doi:10.1063/1.3326077]